Three-dimensional occlusal and interproximal contact detection and display using virtual tooth models

ABSTRACT

Occlusal contact between upper and lower virtual three-dimensional teeth of a patient when the upper and lower arches are in an occlused condition are determined and displayed to the user on a user interface of a general purpose computing device. Various techniques for determining occlusal contacts are described. The areas where occlusal contact occurs is displayed on the user interface in a readily perceptible manner, such as by showing the occlusal contacts in green. If the proposed set-up would result in a interpenetration of teeth in opposing arches, such locations of interpenetration are illustrated in a contrasting color or shading (e.g., red). The ability to calculate distances and display occlusal contacts in a proposed set-up assists the user in planning treatment for the patient. The process can be extended to interproximal contact detection as well. The concepts also apply to dental prosthetics, such as crowns, fillings and dentures.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation in part of U.S. patent application Ser. No.09/835,039 filed Apr. 13, 2001, now U.S. Pat. No. 6,648,640, which is acontinuation-in-part of U.S. patent application Ser. No. 09/560,640filed Apr. 28, 2000, now abandoned, and Ser. No. 09/451,609 filed Nov.30, 1999, now U.S. Pat. No. 6,250,918. The entire contents of each ofthe related applications and patents is incorporated by referenceherein.

BACKGROUND OF THE INVENTION

A. Field of the Invention

This invention relates generally to the fields of dentistry andorthodontics. More particularly, the invention relates to methods forevaluating the areas of contact, and near contact, between upper andlower teeth when the upper and lower arches are in a closed or occludedcondition. Knowledge of such areas of contact (“occlusal contacts”herein) is helpful in planning orthodontic treatment. The presentinvention provides methods of determining and displaying such occlusalcontacts using a computer and three-dimensional virtual models of teeth.

B. Description of Related Art

In orthodontics, a patient suffering from a malocclusion is typicallytreated by bonding brackets to the surface of the patient's teeth. Thebrackets have slots for receiving an archwire. The bracket-archwireinteraction governs forces applied to the teeth and defines the desireddirection of tooth movement. Typically, the bends in the wire are mademanually by the orthodontist. During the course of treatment, themovement of the teeth is monitored. Corrections to the bracket positionand/or wire shape are made manually by the orthodontist.

The key to efficiency in treatment and maximum quality in results is arealistic simulation of the treatment process. Today's orthodontistshave the possibility of taking plaster models of the upper and lowerjaw, cutting the model into single tooth models and sticking these toothmodels into a wax bed, lining them up in the desired position, theso-called set-up. This approach allows for reaching a perfect occlusionwithout any guessing. The next step is to bond a bracket at every toothmodel. This would tell the orthodontist the geometry of the wire to runthrough the bracket slots to receive exactly this result. The next stepinvolves the transfer of the bracket position to the originalmalocclusion model. To make sure that the brackets will be bonded atexactly this position at the real patient's teeth, small templates forevery tooth would have to be fabricated that fit over the bracket and arelevant part of the tooth and allow for reliable placement of thebracket on the patient's teeth. To increase efficiency of the bondingprocess, another option would be to place each single bracket onto amodel of the malocclusion and then fabricate one single transfer trayper jaw that covers all brackets and relevant portions of every tooth.Using such a transfer tray guarantees a very quick and yet precisebonding using indirect bonding.

However, it is obvious that such an approach requires an extreme amountof time and labor and thus is too costly, and this is the reason why itis not practiced widely. The normal orthodontist does not fabricateset-ups; he places the brackets directly on the patient's teeth to thebest of his knowledge, uses an off-the-shelf wire and hopes for thebest. There is no way to confirm whether the brackets are placedcorrectly; and misplacement of the bracket will change the directionand/or magnitude of the forces imparted on the teeth. While at thebeginning of treatment things generally run well as all teeth start tomove at least into the right direction, at the end of treatment a lot oftime is lost by adaptations and corrections required due to the factthat the end result has not been properly planned at any point of time.For the orthodontist this is still preferable over the lab processdescribed above, as the efforts for the lab process would still exceedthe efforts that he has to put in during treatment. And the patient hasno choice and does not know that treatment time could be significantlyreduced if proper planning was done.

U.S. Pat. No. 5,431,562 to Andreiko et al. describes a computerized,appliance-driven approach to orthodontics. In this method, certain shapeinformation of teeth is acquired. A uniplanar target archforrn iscalculated from the shape information. The shape of customized bracketslots, the bracket base, and the shape of an orthodontic archwire, arecalculated in accordance with a mathematically-derived target archform.The goal of the Andreiko et al. method is to give more predictability,standardization, and certainty to orthodontics by replacing the humanelement in orthodontic appliance design with a deterministic,mathematical computation of a target archform and appliance design.Hence the '562 patent teaches away from an interactive, computer-basedsystem in which the orthodontist remains fully involved in patientdiagnosis, appliance design, and treatment planning and monitoring.

More recently, in the late 1990's Align Technologies began offeringtransparent, removable aligning devices as a new treatment modality inorthodontics. In this system, a plaster model of the dentition of thepatent is obtained by the orthodontist and shipped to a remote appliancemanufacturing center, where it is scanned with a laser. A computer modelof the dentition in a target situation is generated at the appliancemanufacturing center and made available for viewing to the orthodontistover the Internet. The orthodontist indicates changes they wish to maketo individual tooth positions. Later, another virtual model is providedover the Internet and the orthodontist reviews the revised model, andindicates any further changes. After several such iterations, the targetsituation is agreed upon. A series of removable aligning devices orshells are manufactured and delivered to the orthodontist. The shells,in theory, will move the patient's teeth to the desired or targetposition. Representative patents describing the Align process includeU.S. Pat. Nos. 6,217,325; 6,210,162; and 6,227,850, which areincorporated by reference herein.

Other patents addressed to planning treatment for a patient includeDoyle, U.S. Pat. No. 5,879,158, Wu et al., U.S. Pat. No. 5,338,198 andSnow et al., U.S. Pat. No. 6,068,482.

Orthodontics and dentistry involves the three-dimensional spatialpositioning of teeth to get the best possible fit. Critical to thesuccess is the relative position of the teeth within the arch and withthe opposing arches. The determinants of these relationships is drivenby both the location and shape/form of the teeth. Although teeth may beideally localized spatially their fit may be poor because the shape ofthe teeth is improper. Determination of the fit between teeth can bebest estimated by defining the contact points/areas between them.Therefore, if the teeth are located correctly and the contact points arenot, it may be assumed there are discrepancies in the shape of theteeth. Location of these discrepancies is vital to achieve the desiredocclusion.

Present approaches to defining or identifying these discrepancies are atbest empirical. In current orthodontic and dental practice, occlusalcontacts are determined by an orthodontist or dentist by using a colorcoated, thin plastic sheet known as “articulating paper”. The patient“bites” onto this foil, and the color is transferred onto the toothsurface, thus indicating where teeth have occlusal contact. Thistechnique is contact-based and provides no quantitative data in terms ofdegree of poor fit.

In accordance with one aspect, the present invention provides for asimulation of this determination and display of occlusal contact usingcomputer techniques and a virtual model of the patient's dentition. Thedetermination and display of the occlusal contacts during treatmentplanning, prior to initiating treatment, allows for the orthodontist tobetter optimize the set-up on the computer. For example, theorthodontist may realize that the set up should be modified by movingone or more teeth relative to the opposing arch to provide for betterocclusal contact or prevent a collision between teeth during movement ofthe teeth from initial to finish positions. Once this more optimal toothset up has been determined, an appliance to move teeth to the desiredpositions can be designed and fabricated. The present invention isapplicable to appliance systems generally and is not limited to abracket and wire approach to straightening teeth.

SUMMARY OF THE INVENTION

In a first aspect, a method is provided for determining the proximity ofteeth of upper and lower jaws of a patient. The method includes thesteps of:

-   -   a) storing data representing three-dimensional models of teeth        from the upper and lower arches of the patient in a memory        associated with a computer; and    -   b) determining, with the computer and the models, distances        between surfaces of teeth in one of the upper and lower arches        and surfaces of teeth in the other of the upper and lower arches        when the teeth of the arches are in an occluded condition        representing an occlusion of the patient. Various possible        methods for determining the distances between surfaces of the        teeth in the upper and lower arches are contemplated and        described in detail below.        From these measurements of distances, it is possible to        determine the locations on the tooth surfaces where the teeth        are in contact, where the teeth are nearly in contact, and where        one or more teeth from one arch may intrude into a tooth or        teeth in the opposite arch. For example, a contact may be        defined as occurring when the distance between the surfaces is        less than a predetermined threshold, such as 0.1 mm. Negative        values of the distance can be associated with interpenetration        or intrusions of one tooth into the opposite tooth.

Thee distance measurements can be assigned to the various locations onthe tooth surfaces from which the measurements are taken. It is thenpossible to illustrate locations where contact occurs on a userinterface, such as a computer workstation having a display screen. Theworkstation typically includes a treatment planning program thatincludes the occlusal contact determination feature. Thus, in apresently preferred embodiment, the method further comprising the stepsof providing a user interface for displaying the three-dimensionalmodels of the teeth, displaying all or a portion of at least one of theupper and lower arches on the user interface, and indicating on themodels information associated with the calculations. For example, theareas where contact occurs can be illustrated in one color (e.g.,green), and areas in which intrusion would occur can be illustrated in asecond color (e.g., red). As an alternative, the distance calculationscan be represented in tabular or other format as numerical distanceinformation for selected portions of the teeth.

The orthodontist will typically perform the method of the presentinvention as one tool in evaluating a proposed set-up for the patient.Based on the measurements of distances between the teeth, and thepossible presence of intrusions, he or she can operate the treatmentplanning software to move the teeth relative to each other to provide amore optimal set-up. Alternatively, the orthodontist may be satisfiedwith the set-up and can deal with the intrusions by grinding away aportion of one or the other tooth involved in the intrusion so as toeliminate the intrusion.

In another aspect, a method is provided for evaluating a proposed set-upof teeth in planning treatment for an orthodontic patient. The methodcomprises the steps of:

-   -   a) obtaining a three-dimensional digital model of the teeth of        the upper and lower arches;    -   b) moving the digital models of the teeth to a proposed set-up        for treating the patient;    -   c) calculating distances between portions of the teeth in the        upper and lower arches when the teeth are positioned in an        occluded condition; and    -   d) displaying the virtual models of the teeth to a user in a        manner such that a user can readily distinguish portions of the        teeth in the upper and lower arches in which the distance        between the portions is less than a predetermined threshold.

Occlusal contact information can be determined statically, ordynamically. For example, in another embodiment of the invention theteeth are moved from an open to a closed condition and the initial areasof contact are determined and displayed. As another example, theocclusal contacts can be determined by simulating a chewing motion ofthe upper and lower arches and calculating distances between the teethduring the chewing motion to find the areas of contact between the upperand lower arches.

As another embodiment of the invention, the feature of determiningdistances between teeth and displaying such information can be used todetermine interproximal points of contact. The feature can be extendedto determining interproximal and occlusal contact for virtual prostheticdevices, such as crowns and bridges. The determination of such contactson a compute allows the clinician to evaluate the prosthetic device andoptimize its, shape, position and/or orientation so as to maximize itsinterproximal and occlusal relationship to adjacent and opposing teeth.

In still another aspect, the use of contact information can enable a“magnetic” function by which teeth are automatically positioned in closeproximity or touching contact with an adjacent tooth or an opposingtooth. In particular, a method is provided of manipulating virtual teethon a user interface of a general-purpose computer, the user interfaceincluding a display and a pointing device. The virtual teeth includes afirst virtual tooth and a second virtual tooth, the second virtual toothcomprising either an adjacent tooth or an opposing tooth of the firstvirtual tooth. The method includes the steps of selecting the firstvirtual tooth with the pointing device, moving the pointing device whilethe first virtual tooth is selected so as to drag the first virtualtooth in the direction of the second virtual tooth, automatically movingthe first virtual tooth so as to place the first virtual tooth intoproximity with the second virtual tooth without requiring said user todrag the first virtual tooth into proximity to the second virtual tooth.This feature simulates a magnetic attraction of the first virtual toothto the second virtual tooth. The feature makes design of a proposedset-up for the patient easier and less time consuming.

These and many other aspects and features of the various inventionsdisclosed and claimed herein will be explained in more detail in thefollowing description of a presently preferred implementation.

BRIEF DESCRIPTION OF THE DRAWINGS

Presently preferred embodiments of the invention are described below inconjunction with the appended drawing figures, where like referencenumerals refer to like elements in the various views, and wherein:

FIG. 1 is a view of a set of virtual three-dimensional tooth modelsrepresenting the teeth of the lower arch of a patient, as they might bepresented on the screen of a computer. The teeth have been moved from amaloccluded condition to a proposed set-up or finish position using atreatment planning program. The portions of teeth that would haveocclusal contact with the teeth on the upper arch are shown in acontrasting color or shading to assist the orthodontist in evaluatingthe proposed set-up.

FIG. 2 is another view of a portion of the upper and lower arches of thepatient in the proposed set-up, with the view taken from the lingualside of the arches, showing the spatial relationship of the teeth of theupper and lower arches with the occlusal contacts on the teeth of theupper arch shown in a contrasting color or shading

FIG. 3 is a view of a molar of a virtual three dimensional tooth withone portion of the tooth cusp shown on one color (e.g., green) to showareas which are occlusal contact with the opposite tooth and anotherportion shown in a second color (e.g., red) showing areas in which theopposite tooth would interpenetrate the tooth in the proposed set-up,thereby indicating the need to revise the treatment plan.

FIG. 4 is a schematic representation of a tooth in the upper and lowerarches, illustrating one method to determine the distance betweenportions of the teeth.

FIG. 5 is a schematic representation of a tooth in the upper and lowerarches, illustrating an alternative method to determine the distancebetween portions of the teeth.

FIG. 6 is a schematic representation of a tooth in the upper and lowerarches, illustrating one of the disadvantages to the method of FIG. 5.

FIG. 7 is a schematic representation of a tooth in the upper and lowerarches, illustrating an alternative method to determine the distancebetween portions of the teeth.

FIG. 8 shows a set of teeth in one arch with parallel planesintersecting the teeth to form parallel lines, illustrating onetechnique for determining the closeness of teeth; the parallel lines canbe created vertically to determine the separation between teeth in theupper and lower arches.

FIG. 9 is a cross-section through the teeth of FIG. 8 along one of theplanes illustrated in FIG. 8.

FIG. 10 is an illustration of a scanner and computer system that can beused in the practice of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Overview

The determination and display of occlusal contacts between teeth in theupper and lower jaws in accordance with a preferred embodiment of theinvention makes use of three-dimensional virtual models of teeth. Thevirtual models of teeth are stored in a memory and available to ageneral-purpose computer. As is known in the art, virtual models ofteeth of a patient can be obtained by using a laser scanner to scan aphysical model of the dentition. Alternatively, the teeth can be scannedin vivo, or a model of the dentition can be scanned, by a hand-heldscanner such as the type described in published PCT application ofOraMetrix, Inc., PCT/US01/11969, publication no. WO 01/80761, the entirecontents of which is incorporated by reference herein.

Once the teeth have been scanned, the three-dimensional scan data can berepresented in a a computer and displayed to the user as athree-dimensional model. There are a variety of techniques known in theCAD/CAM art for representing a three-dimensional surface, and the choiceof a particular technique or format for representation of the virtualteeth is not important. The present invention will be described incontext of a representation of a surface as a set of points that definecontiguous three-dimensional triangular shaped surface segments. Otherrepresentations of a surface such as Nonuniform Rational B Splines(NORBS) can be used. A volumetric description using voxels (a techniqueknown in the art) automatically describes a surface and that is anotherpossibility.

After the dentition, or a physical model of the dentition, has beenscanned, it is helpful to separate the individual teeth from the rest ofthe anatomical structures (e.g., gingival tissue) so that individualteeth can be represented as independent, individual three-dimensionalvirtual objects. This is described in the above-referenced PCTapplication of OraMetrix. Once the teeth have been separated into suchindividual objects, CAD/CAM techniques can be used to move the teethrelative to each other to arrive at a set-up for the patient. Aparticularly advanced and highly preferred treatment planning softwareapplication that performs these and other tasks is described at lengthin the above-referenced PCT application of OraMetrix. The softwarepreferably provides the user with the ability to display the archesindividually, or together, either alone or in an occluded condition. Therelative position of the arches in the occluded position is preferablyuser-specified by the treatment planning software. Since the techniquesused to moved teeth and/or arches relative to each other are alreadydescribed in the patent literature, the details are omitted from thepresent discussion for the sake of brevity.

As noted above, once the teeth are represented as virtual objects andmoved to a proposed set-up representing an ideal archform for thepatient, it is possible to evaluate the set-up under a variety ofcriteria, prior to initiating treatment. One possible criteria forevaluation is the occlusal contacts. The present method of determiningand displaying occlusal contact information preferably involvesmeasuring the distance from the teeth in one arch to the teeth in theother arch, with the arches in an occluded condition. More particularly,the method involves measuring or determining the distance between aplurality of locations (points or surfaces) of one tooth and the closestlocations (i.e., surfaces or points) of teeth in the opposite arch.

In a preferred implementation, for each point (vertex) of the surface ofthe digital tooth model, the closest surface point of an opposing toothis determined. The distance can be calculated using the computer, sincethe relative positions of the teeth of both arches in three-dimensionalspace is known and stored in the computer. Once the distance has beencalculated, the tooth surfaces in which the distance is less than apredetermined threshold can be illustrated or displayed to the user in amanner that allows the user to readily perceive such locations. Forexample, the tooth surfaces which are less than 0.1 mm apart are deemedto be “occlusal contacts” and are colored or given a shading. In anexample in which the surface of the teeth is represented a contiguoustriangle surfaces, we can assign a color (e.g., green) or a particulartype of shading to the triangles that are associated to the point orsurface at which the distance was calculated and the minimum distance tothe opposite tooth is less than the threshold.

FIG. 1 shows a three-dimensional virtual model of the teeth of thepatient, consisting of individual and independently moveable toothobjects or teeth 10, which have been moved by a treatment planningsoftware application to a proposed set-up. The teeth include cusps 12.The distance between locations on the surface of the teeth in the lowerarch to the teeth in the upper arch has been performed when the virtualmodel of the upper and lower arches are moved to an occluded position.The distances which are less than a threshold value, such as 0.45 mm,are shown on the monitor of the workstation in a contrasting color orshading as occlusal contact regions 14.

In one possible embodiment, it is possible to use a smooth transition oftooth color to green. Points that are further away than 0.45 mm from theopposing tooth are colored purely in tooth color. Points that contactthe opposing tooth are colored in pure green. All other points receive acolor that is between tooth color and green, according to the distance.Thus, we have a continuous transition from tooth color to green. Thegranularity of this transition may be limited depending on the typicalsize of the triangles defining the surface, and the abilities of therendering engine software that is being used to display those trianglesat the computer monitor. Some rendering engines do not allow definitionof colors within a triangle, but rather it is only possible to definecolors for the vertex points defining a triangle and the renderingengine will then color the triangle accordingly. However, if we had afiner triangle resolution, we would have a very smooth transition fromtooth color to green.

FIG. 2 shows another view of the upper and lower arches in the occlusedcondition, with the occlusal contacts shown as regions 14.

One possible color scheme for representing the occlusal contacts is asfollows. If the distance between the opposing tooth and the point orportion of the tooth to be examined is smaller than 0.45 mm, the area 14is shaded green. The value of 0.45 is somewhat arbitrary, and preferablycan be user specified by modifying a variable in a suitable screen ofthe treatment planning program. The smaller the value is, the smallerthe area displayed as occlusal contact would be. Since, mathematicallyspeaking, only one point really contacts the opposing tooth, we wouldonly have tiny dots if we would indicate only points that actually havecontact. The value of 0.45 mm has been found to provide a more useableresult.

If the distance is negative, this would indicate interpenetration, thatis, a portion of one tooth has collided with the opposing tooth suchthat it physically projects into the other tooth. This is an undesirableoutcome when planning treatment, clinically speaking. Thus, when anorthodontist is planning treatment and evaluating a proposed treatmentplan, whether or not such interpenetration between teeth of opposingarches would result is of great interest to the orthodontist. Thepresent method enables such situations to be determined and displayed tothe user. For example, we can show such interpenetration or negativedistance values, using a red color to indicate the affected toothportions. In FIG. 3, the molar 10 has occlusal contact portions 14 and aregion 16 shown in red which would be penetrated by the opposite toothin the other arch should the proposed treatment plan be implemented andan occlusion occur. Obviously, this is undesirable since in realityteeth cannot penetrate each other. Such a se-up would thereforerepresent an unrealistic scenario. The red region 16 thus alerts theorthodontist to the problem. The problem can be corrected by adjustmentof the plan by simulation of movement of the affected tooth or teethrelative to each other to eliminate the interpenetration or by grindingthe affected portions of the tooth or teeth.

When operating the treatment planning software for a patient with amalocclusion, the software is developed such that the user is normallyprevented from moving teeth into one another when designing a toothfinish position. However, sometimes teeth have features that may need tobe ground by the orthodontist to receive good occlusion. In such a case,the treatment planning software allows the user to override theinterpenetration prohibition feature, so that the user can indeed moveteeth into one another. The red spot 16 of FIG. 3 representing aninterpenetration tells the orthodontist very clearly and exactly, whichportion has to be ground away. The orthodontist can do this at a veryearly state of treatment. This is an advantage, since we allow the teethto readily move into the desired occlusion once a disturbing feature isground, instead of waiting and finding out very late that grinding isrequired.

In a possible alternative implementation, the software virtually“subtracts” or deletes the opposing tooth from the tooth to be ground tothereby modify the three-dimensional virtual form of the tooth to beground. This subtraction or deletion can be done using known CAD/CAMtechniques. The modified tooth shape is then displayed to the user. Thisprocedure allows the orthodontist to determine exactly not only whicharea needs to be ground, but to which shape. In yet anotherimplementation, the orthodontist grinds the tooth carefully, scans it,compares the scan data to the shape of the modified virtual tooth model,and thus determines whether and where further grinding is required.

Preferred Implementation of Contact Detection

There are several ways to determine occlusal contacts. We have preferreda simple and fast approach, which is as follows. With reference to FIG.4, from each vertex point 20 (corner point of a triangle making up oneelement of the surface), a ray or vector 18 is constructed running alonga pre-defined direction. In a preferred implementation, this directionis parallel to the tooth axis, which is defined for each tooth as acentral axis extending the length of the tooth through the center of thecusp. Other options are discussed further below. Each ray 18 is sentboth to the outside and the inside of the tooth, as shown in FIG. 4.Then, we determine where the vector intersects the surface of opposingteeth 10′. These points of intersection (actually, small trianglesurfaces) are shown as points 22 in FIG. 4. The distance from the vertexpoint 20 to the intersection 22 is calculated. According to the colorscheme, the triangles associated to the vertex point 20 are assigned acolor depending on the distance and the mathematical sign(positive/negative). For example, the surfaces associated with vertexpoint 20 with a negative value are colored red. All surfaces 20 with apositive value less than 0.45 mm are colored green. The surface wherethe distance is greater than or equal to 0.45 mm are not colored. Thevirtual models of the upper and lower arches are displayed (typicallyseparately) with the color information on a user interface of theworkstation implemnenting the program. See, for example, the views shownin FIGS. 1–3.

This procedure is performed for every surface element (triangle) of thetooth. The procedure is also done for each tooth in one of the twoarches. In one possible embodiment the user is able to modify theseparation distance variable that is indicative of an ocelusal contact(e.g., 0.45 mm). Alternatively, the separation distance can beprogrammed as a fixed parameter.

We have selected the approach of FIG. 4 because it is very fast,computationally speaking. An alternative, more sophisticated approachwould be to send the rays in the direction of a normal vector to thetooth surface. This is shown in FIG. 5, where the rays 18 are directednormal to the tooth surface 10. This alternative would require moretime, since the normal vectors 18 of FIG. 5 would have to be calculatedfor each vertex point. However, since there is no normal vector to apoint, we would have to calculate the normal vector to each trianglesurface element that the vertex belongs to, and then calculate themedian vector. The preferred embodiment described in conjunction withFIG. 4 avoids these additional computational steps and thus is quickerto perform using a state of the art microprocessor. As processing speedsimprove, the alternative method of FIG. 5 may become perfectly suitableand thus may represent a better and more accurate alternative.Additionally, the process of FIG. 5 may not by default create betterresults, as is shown in FIG. 6. Here, the normal vector 18 from point 20barely misses the tooth surface 10′, whereas the method of FIG. 4 wouldhave definitely located the surface immediately above the point 20.

An ideal method for determining the closest surface of the oppositetooth is shown in FIG. 7. The method involves creating a virtual sphere30 around each point in the tooth 10, and increasing the diameter D ofthe sphere in suitable increments (e.g., 0.01 mm) until the sphereintersects with an opposing surface. The value of D then indicates theproximity of the point of the tooth with the opposite tooth and thisvalue is stored for the point. The process is done for all the pointscomprising the tooth surface. The treatment planning software thendisplays the model of the teeth with all surfaces corresponding to thepoints for which 0<D<0.45 mm displayed in green, and all surfacescorresponding to the points for which D<0 displayed in red.

The algorithms described thus far are applicable approaches forthree-dimensional virtual objects that have a surface representationcreated by vertex points and connecting surface elements (trianglesetc.). However, there are other acceptable mathematical techniques forrepresenting arbitrary three-dimensional shapes in a computer. Thetechniques include volumetric descriptions (IGES format), and NonuniformRational B Splines (WRBS). These techniques could be used. A personskilled in the art would not have difficulty to design an appropriatealgorithm for determining occlusal contacts using these or othertechniques.

One example would be the “contour line” algorithm, which will bedescribed in conjunction with FIGS. 8 and 9. At the tooth surface,contour lines 32 are calculated in predefined planes (e.g. 0.1 mm). FIG.9 is a cross-section through the teeth along one of the contour lines32. Within each plane, such as shown in FIG. 9, a check is performed tosee if contour lines of adjacent teeth intersect. This approach couldalso be used to detect occlusal contacts. In particular, a set ofparallel planes are defined that are oriented in a vertical directioninstead of a horizontal direction. The planes will intersect thesurfaces of the upper and lower teeth, thereby forming two lines on eachplane, one for the tooth in the lower arch and the other for the toothin the upper arch, analogous to the lines shown in the cross section ofFIG. 9. The software then looks for areas in which the separationdistance between the two lines is less than a threshold. If the twolines intersect, the teeth touch. If a bounded or closed volume isformed by the two lines, then an interpenetration of the teeth hasoccurred. The contour line algorithm can be used with any kind of 3Dobject description. The technique of FIG. 9 can be used to determine theinterproximal distances between teeth, as discussed further below.

Another possible embodiment uses an “octree” data structure (a knowntechnique) to describe the shape of teeth. This further eases the taskof contact detection, since the data is organized in spatial cells andthe amount of data needed to represent the surface is reducedsignificantly, resulting in reduced time to calculate occlusal contacts.

One possible computer and scanner arrangement for practicing theinvention is shown in FIG. 10. An orthodontic clinic 50 is equipped witha hand-held scanner 52 which is used for either in-vivo scanning of apatient or scanning a physical model 54 of the upper and lower arches.The hand-held scanner 52 supplies scan data to a scanning node orcomputer 56 which processes the scan data to derive three-dimensionalshape data from the arches. This data is supplied to a general-purposecomputer 58 having a user interface 60. The computer 58 is equipped withor accessible to a memory (not shown) storing the tooth models and aninteractive treatment planning software. The software separates theindividual teeth from the surrounding anatomical structures and allowsthe user to interactively and selectively move the teeth to a desireddental archform for both upper and lower arches. One possible embodimentof a scanner and workstation providing treatment planning software forvirtual teeth of the upper and lower arches is described in the PCTapplication of OraMetrix, Inc., referenced previously. The workstationalso includes occlusal contact and detection tools as described abovethat allow the orthodontist to view the virtual teeth 10 on theworkstation with the occlusal contacts illustrated in a contrastingcolor (such as red or green).

The workstation or computer 58 is shown coupled via the Internet 62 to aremote facility having an orthodontic server 64. In one possibleembodiment, the scan data from the scanner 52 is sent to the remotefacility and the orthodontic server 64 generates an initial treatmentplan for the orthodontist to review. The occlusal contact detection anddisplay can of course occur at the orthodontic server. Similarly thevirtual model of the teeth may be sent electronically to other locationsand shared and viewed by other health care professionals that aretreating the patient.

The collision or contact detection features described above enableanother useful feature in planning treatment for a patient. Thisadditional feature is that when one virtual tooth is moved to a newlocation, the tooth is automatically moved into close proximity ortouching contact with the adjacent or opposite tooth. This featurestreamlines the process of designing proposed set-ups for a patient, asit keeps all the teeth together and places them in contact in the arch.This technique is referred to herein as a “magnetic” function.

The collision detection/prevention functionality is possible due to afeature of the Windows® operating system. Whenever the mouse is moved,the operating system not only places the mouse pointer at the respectivelocation at the screen. It also sends a message to the program that ownsthe window where the mouse pointer is currently being moved over. Thismessage is sent over and over, as long as the mouse is on the move. Themessage includes the current location of the mouse pointer. The samething happens (obviously only once), when you click the mouse or releasethe mouse. This functionality is a fundamental aspect of 3D softwarerunning on a Windows® operating system. In our implementation, the userclicks the mouse. We store the respective location of the mouse pointer.The user moves the mouse. The operating system continuously sendsmessages containing the current location of the mouse pointer. Ourpresently preferred treatment planning software calculates the distancethat the mouse pointer has covered and the direction, and we then movethe 3D object that is currently selected respectively, and immediatelydisplay the new location on the screen. This is one way how the user canmove a virtual object such as a tooth. However, before simply moving theobject in accordance with the mouse movements, we can perform any kindof calculations, such as distance calculations to opposing or adjacentteeth. If the collision prevention feature is enabled or active, wecalculate the remaining distance to the opposing (or adjacent) tooth. Ifthis distance is smaller than the distance that the user indicated bymouse movement, we simply move the object only according to theremaining distance. To the user, this looks as if the object is hittingthe opposing or adjacent object and cannot move any further.

When the magnetic functionality is activated, and the user has selecteda tooth and starts moving it by dragging with the mouse, we calculatethe remaining distance to the opposing tooth and immediately move thetooth over the complete distance, no matter how far the mouse has reallybeen moved. So the selected tooth will immediately get in contact withits opponent. This calculation is performed on all mouse movements,whether they indicate translations or rotations. The distance betweenthe selected tooth and its opponent is kept to zero, so that the toothappears to be “magnetically” attached to its opponent. Alternatively,the tooth could be placed in close proximity, that is, separated by someamount such as 0.01 mm. In one possible embodiment, the user is allowedto modify the separation distance, such as by clicking on a suitableicon and selecting a new value for the separation distance.

Other Embodiments and Features

A. Initial Occlusal Contact Determination and Occlusal Contactdetermination During Treatment

The occlusal contact determination can be made for the initial(maloccluded) condition of the patient's teeth. The patient's teeth arescanned (either directly or from a physical model) and then the scandata is converted into a 3D representation of the dentition. A biteregistration scan is performed, and the three-dimensional relationshipof the upper and lower arches of the teeth is obtained. The virtualmodels of the upper and lower arches can now be positioned in anoccluded condition and the process described above can be performed tofind the occlusal areas.

The identification and display of the occlusal contacts in the initialcondition is helpful in evaluating a proposed treatment plan because itenables the practitioner to compare the initial and proposed treatmentplans in terms of occlusal contacts. For example, the user interfacecould be organized into a split screen to show the occlusal contacts forthe lower jaw in the initial condition on the left hand side and theocclusal contacts in the proposed treatment on the right hand side ofthe screen.

The determination of occlusal contacts can also be obtained anddisplayed at any time during treatment. During treatment, the upper andlower arches are scanned and a bite registration scan is taken.Preferably, for a bracket and wire type of treatment regime, the scansare performed in vivo using a hand-held 3D scanner such as described inthe published PCT patent application of OraMetrix, Inc. citedpreviously. Again, a qualitative assessment of the occlusal contacts canbe made to more completely assess the progress of treatment, and thecurrent stage of occlusal contacts can be compared to the expectedtreatment outcome and initial occlusal contacts to verify that thetreatment is progressing properly. In the event that the occlusalcontact detection and display results in a desire to change thetreatment, the treatment plan can be revised and the patient fitted witha modified orthodontic appliance. For example, the wire may be given amodified geometry to move the teeth into a more optimal position toincrease the occlusal contact area.

B. Dynamic Detection of Occlusal Contacts

The present invention also provides for the ability to determine anddisplay occlusal contacts dynamically, that is, the order and locationat which the contacts occur when the patient's jaw are moved dynamicallyfrom an open to a closed condition. The 3D models of the upper and lowerarches can be moved relative to one another to simulate closing of thejaw or a chewing motion. This simulation can be done for initialcondition of the arches, or for the arches when the teeth are movedrelative to each other in a proposed treatment plan. The dynamic modelof the motion of the mandible relative to the maxilla during occlusionor chewing can be obtained via a variety of imaging techniques,including video, X-ray, or successive scans of the upper and lowerarches as the patient moves their teeth. The determination of where theteeth are coming into contact during an occlusion or during a chewingmotion yields clinically important information that is helpful inplanning treatment, revising an initial treatment plan, or inconsideration of whether additional medical care is recommended for thepatient.

Thus, in another aspect, a method is provided for determining theproximity of teeth of upper and lower jaws of a patient comprising thesteps of:

-   -   a) storing data representing a three-dimensional model of teeth        from the upper and lower arches of the patient in a memory        associated with a computer;    -   b) simulating motion of said upper and lower arches relative to        each other; and    -   c) calculating, with said computer and model, distances between        surfaces of teeth in one of said upper and lower arches and        surfaces of teeth in the other of said upper and lower arches        during said simulation of motion.

Information regarding the calculations can be illustrated to the user ona display associated with the computer, such as showing the initialcontacts in one color, and all of the other occlusal contacts in acontrasting color or shading. The display of contact information can bea static display of the teeth or in a dynamic simulation of the motion.

C. Tooth Wear and Occlusal Contact Monitoring

Many persons suffer from bruxism, a condition in which they grind theirteeth, typically while they are asleep. Over time, the tooth enamel isworn down, which can lead to other problems for the patient includingdecay or disease of the tooth. Detection and monitoring of tooth wear isan important diagnostic feature provided in one aspect of the presentinvention. The progress of the bruxism can be monitored by taking a scanof the patient initially, taking a second scan at a later point in time,and comparing the tooth models of selected teeth or all the teeth beforeand after. For example, a subtraction feature is employed by which thevirtual model of a tooth at the later stage is subtracted from the modelat the initial stage, with the difference being the portion of the tooththat has been worn away. A method of monitoring tooth wear is thusprovided, comprising the steps of obtaining a first three-dimensionalvirtual model of a portion of the patient's dentition at a first pointin time, obtaining a second three-dimensional virtual model of saidportion of the patient's dentition at a second, later point in time; andcomparing said first and second virtual models to each other. The stepof comparison can be a subtraction operation, which is typicallyprovided in CAD/CAM software. The method continues with the step ofidentifying, from step of comparison, portions of the firstthree-dimensional virtual model that are no longer present in saidsecond three-dimensional model due to wear of the dentition. Forexample, the identifying step could be performed by illustrating on thedisplay screen the first three-dimensional model with the areas wornaway in a contrasting color or shading.

Alternatively, tooth wear can be monitored by measuring occlusalcontacts at two different points in time. By measuring the occlusalcontacts of the teeth both at an initial stage of treatment and at alater point in time, the occlusal contact areas can be compared to eachother. One would typically expect that the occlusal contact surface areawould increase in time, particularly in the areas where bruxism isoccurring. The evaluation of before and after occlusal contacts can bemade qualitatively, using a subjective visual assessment of the occlusalcontacts as displayed on a monitor, or it can be done quantitatively.For quantitative occlusal contact analysis, measurement tools such asfine grid can be placed over the region of the occlusal contacts and thesurface area of the occlusal contact measured or calculated either by ahuman operator or automatically using the computer.

The process can be extended to measurement of gingival recession anderosion caused by tooth brushing or chemical erosion.

D. Contacts Between Teeth

The distance detection algorithms described herein can also be used todetermine the interproximal contact points between teeth, either in aninitial situation or in a proposed treatment plan for the patient.Optimal interproximal contact points between teeth is important to avoidimpaction of food between the teeth. The interproximal contact pointscan be identified by the algorithms explained previously for opposingteeth, except that the distance measurements are being made to theadjacent tooth. The technique of establishing parallel planes anddetermining where the planes intersect the teeth, as shown in FIGS. 8and 9, yields a set of lines, one line for each tooth. The distancebetween the lines is indicative of the interproximal distance. This is aparticularly useful approach. The interproximal contact points can thenbe displayed on the monitor of the workstation and evaluated by theuser.

The ability to quantitatively measure and display interproximal contactpoints is a distinct advantage for an interactive treatment planningsoftware program. In particular, it enables the user to position eachtooth relative to its neighbor in a manner such that the interproximalcontacts are optimized on a tooth by tooth basis. The treatment planningprogram preferably provides the orthodontist with the ability to moveeach tooth relative to another tooth, for example rotate about the toothaxis, tilt the tooth or move it up or down to optimize the interproximalrelationship with the adjacent teeth. The visual display ofinterproximal contacts (such as in a green color where the separationdistance is less than a threshold such as 0.1 mm) gives the userimmediate feedback on the quality of the setup. Furthermore, as a givenvirtual tooth is moved, the software is preferably programmed such thatthe occlusal contact display changes immediately to give instant visualfeedback as to the effect of tooth movement on occlusal contacts.

E. Restorative Dentistry and Dental Prosthetics

The occlusal contact and interproximal contact detection and display canalso be a highly useful feature in planning restorative dentistry. Forexample, if no orthodontic treatment is planned but the patient is goingto be given a crown, inlay, or other prosthetic device, the design andmanufacture of the prosthetic device can be optimized in terms ofproviding interproximal and occlusal contact. This is achieved byscanning the patient's dentition, including a bite registration scan,and designing the shape of the prosthetic device as a virtualthree-dimensional object on the computer. The design of the prostheticdevice takes into account the interproximal (and occlusal) relationshipto the other teeth. The three-dimensional shape of the prosthetic isoptimized on the computer so that when it is implanted in the patient itachieves a superior interproximal and occlusal relationship with therest of the patient's teeth.

In the specific case of crowns, crowns are typically made of gold usinga lost wax process in a dental lab. The lost wax process includes anintermediate step of creating a wax model of the crown. The wax modelcan be scanned using a 3D scanner and the crown represented as anindependent three-dimensional virtual object. The virtual object canthen be fitted to a virtual model of the tooth, in effect simulating theinstallation of the crown in the patient. This simulation can occur in aworkstation in the office of the dentist or in the lab. The dentist canevaluate the fit of the crown relative to the other teeth. If thedentist wishes to modify the shape of the crown, he or she canmanipulate the model to add or subtract or otherwise modify the shape ofthe crown. The 3D model can then be exported to a rapid prototypingmachine (such as, for example, stereolithography (SLA), laser 3Dprinting, etc.) for manufacture of a physical model of the crown. Theprocess proceeds with a manufacture of a crown in gold or porcelainhaving the modified configuration.

The process can also be extended to fillings, namely the detection ofocclusal contacts for filings and determination of high spots using thealgorithms described herein. The challenge faced by the dentist is thatas the filling is done the dentist asks the patient to bite down todetect the high spot. Invariably, the pressure from the occlusionfractures the partially set amalgam. Our approach is a contactlessapproach and eliminates that risk. Similarly for crowns, our electronicdetection eliminates any interventional episodes for chairsidecorrection of the crown to ensure better fit.

Similar concepts apply when designing other appliances and prostheticdevices, such as dentures. The process of design can be carried out on acomputer using virtual tooth models and the determination, display andevaluation of interproximal and occlusal contacts can be made on aworkstation using the techniques described herein so as to optimize thedesign of the appliance or device.

The method can be extended to designing and fabricating a set ofdentures for a patient and improving interproximal and occlusal contactof the teeth of the dentures. In this aspect, the method includes thesteps of obtaining a three-dimensional virtual model of teeth of upperand lower arches of the patient. This can be done for example usingtemplate teeth stored in memory (see the published PCT application ofOraMetrix, Inc., cited previously) or from a scan of the patient'steeth. The virtual model is stored in a computer, preferably a computerhaving treatment planning software. The teeth of the upper and lowerarches are moved relative to each other to a proposed arrangement for aset of dentures. Then, using the techniques described in detail herein,the computer calculates distances between surfaces of adjacent teeth andbetween surfaces of opposing teeth with the upper and lower arches in aclosed condition to assess the interproximal relationship and occlusalcontacts of the teeth. The computer displayes information associatedwith calculations on a user interface, such as by showing occlusalcontacts or interproximal contacts in a contrasting color or shading orusing a transition from white to color. The dentist then uses thetreatment planning software to adjust the position of one or more teethto more optimally position of the teeth relative to each other as aresult of the display of contact information. When the optimalarrangement is arrived at, the dentures are fabricated.

Not only can the above method be used for detecting denture contacts, itcan be applied to surgical splints that are implanted in the patient'smouth. The design of the splint can be carried out on a computer and amilling machine can grind them accurately even before insertion.

F. Bracket, Wire, and Appliance Location and Conflicts

The above descriptions of occlusal and interproximal contactdetermination have assumed that one is measuring distance between teeth.The technique can be extended to determining distances between a toothand a portion of an orthodontic appliance, such as a bracket or wire.The technique can also be used for determining the distance betweenopposing brackets in the upper and lower arches or between a bracket andan opposing wire, or between opposing wires. For example, the distancebetween a tooth cusp and the bracket on the opposing tooth is calculatedusing one of the algorithms described previously. The virtual models ofthe upper arches will be typically placed in a closed or occludedcondition when this calculation is performed. The teeth and brackets arepresented as virtual objects on the workstation of the computer with theareas in which the distance between the bracket and tooth is less than athreshold highlighted in a contrasting color or shading or as a smoothtransition in color or shading. Actual collisions between the teeth andthe brackets can also be calculated and displayed. This feature againhelps the user evaluate a proposed treatment plan, including a proposedlocation of brackets on the teeth. The user is preferably able to modifythe location of the virtual brackets on the teeth and run a newsimulation of potential contact or collision between the appliance andthe teeth. The collision or conflict detection process can also beperformed based on actual location of the brackets on the patient'steeth, using a virtual model of the patient obtained from scanning ofthe patient.

Thus, in another aspect, a method is provided for determining potentialconflicts in positioning of an orthodontic appliance on the dentition ofthe patient. The method comprises the steps of obtaining a virtual modelof the upper and lower arches of patient's dentition; positioning avirtual model of an orthodontic appliance on at least one of the archesof the virtual model of the dentition; placing the virtual models of theupper and lower arches in an occluded condition; calculating distancesbetween portions of the virtual model of the dentition and portions ofthe virtual model of the orthodontic appliance, and displaying thevirtual models of the upper and lower arches and the orthodonticappliance on a user interface along with information associated with thecalculations. The process can be extended to conflicts between bracketson opposing teeth, conflicts between brackets and gingival tissue,conflicts between brackets and wires in the opposing arch, and conflictsbetween upper and lower archwires.

Variations from the illustrated technique, methods and apparatus iscontemplated without departure from the scope of the invention. The term“contrasting color or shading” in the claims, in reference to thedisplay of contact information, is intended to encompass the situationin which a transition of color occurs between portions of the toothwhich are not contacts and portions which are (i.e. distance to theopposing or adjacent tooth is less than a threshold), as well as thesituation in which no transition occurs and the portions below thethreshold are illustrated in a contrasting color or shading and theportions above the threshold are illustrated in the usual manner (e.g.,as white objects or in natural color). This true scope is to beascertained by reference to the appended claims.

1. A method for determining the proximity of teeth of upper and lowerjaws of a patient, comprising the steps of: a) storing data representinga three-dimensional model of teeth from the upper and lower arches ofthe patient in a memory associated with a computer; and b) calculating,with said computer and model, distances characterizing the occlusalrelationship between surfaces of teeth in one of said upper and lowerarches and surfaces of teeth in the other of said upper and lower archeswhen said arches are in an occluded condition; wherein said step ofcalculating includes, for a plurality of points on a surface of a tooth,the step of calculating a sphere around each of said points, andenlarging the size of the sphere until the sphere intersects with asurface of a tooth on the opposing arch in said model.
 2. The method ofclaim 1, wherein said step of indicating comprises the step ofdisplaying portions of said model in a contrasting color or shadingrelative to other portions of said model.
 3. The method of claim 1,wherein said step of calculating results in a determination that thedistances between portions of teeth in the upper and lower arches isless than zero, and wherein said portions are illustrated in acontrasting color or shading relative to other portions of said model.4. The method of claim 1, wherein said three-dimensional model of teethcomprises a proposed arrangement of teeth in the upper and lower archesfor planning orthodontic treatment of said patient.
 5. The method ofclaim 1, wherein said step of calculating results in a determinationthat a portion of a tooth of one of said arches intrudes into a portionof a tooth of the other of said arches, and wherein the method furthercomprises the step of displaying on a user interface the said portionsof said tooth in a manner such that a user can readily distinguish saidportions.
 6. The method of claim 1, wherein said data representing athree-dimensional model of teeth comprises data representing an initialmalocclusion of said patient.
 7. The method of claim 1, wherein saiddata representing a three-dimensional model of teeth comprises datarepresenting a state of the patient's dentition during the course oftreatment wherein said teeth have moved from an initial malocclusiontowards a final position and performing step b) for said model of teethrepresenting the dentition during the course of treatment.
 8. The methodof claim 7, further comprising the step of displaying occlusal contactareas for said patient on a user interface as a result of saidcalculating step b).
 9. The method of claim 8, further comprising thestep of performing steps a) and b) for data representing athree-dimensional model of teeth comprising an initial malocclusion, anddisplaying occlusal contact areas for said patient on said userinterface as a result of said calculating step b) performed on saidmodel of teeth comprising an initial malocclusion.
 10. The method ofclaim 8, further comprising the step of modifying a treatment plan forsaid patient based on evaluation of said display of said occlusalcontact areas.
 11. A method for assessing the interproximal relationshipof teeth in an arch of a patient, comprising the steps of: a) storingdata representing a three-dimensional model of teeth from said arch in amemory associated with a computer; b) calculating, with said computerand model, distances characterizing the interproximal relationshipbetween surfaces of a first tooth in said arch to surfaces of a secondadjacent tooth in said arch; wherein said step of calculating includesthe step of calculating a sphere around a plurality of points on asurface of said first tooth in said one arch of said model, andenlarging the size of the sphere until the sphere intersects with asurface of said second tooth; c) providing a user interface fordisplaying said arch; and d) indicating on said display informationassociated with said calculations.
 12. The method of claim 11, whereinsaid step of indicating comprises the step of displaying portions ofsaid first and second teeth in a contrasting color or shading relativeto other regions of said first and second teeth in which said distancebetween said portions is less than a predetermined threshold.
 13. Themethod of claim 11, wherein said step of calculating results in adetermination that the distances between portions of said first andsecond teeth is less than or equal to zero, and wherein said portionsare illustrated in a contrasting color or shading relative to otherportions of said teeth.
 14. The method of claim 11, wherein saidthree-dimensional model comprises a proposed arrangement of teeth forplanning orthodontic treatment of said patient.
 15. The method of claim14, further comprising the step of moving one of said first and secondteeth and repeating steps b) and d).
 16. A method of improvinginterproximal and occlusal contact between a tooth of a patient and aprosthetic device to be installed in the dentition of the patient inproximity to said tooth, comprising the steps of: obtaining athree-dimensional virtual model of a portion of the dentition of thepatient; storing the virtual model of the portion of the dentition in acomputer; storing a virtual model of the prosthetic device in saidcomputer; displaying said virtual model of the portion of the dentitionand the virtual model of the prosthetic device on a user interface, withthe virtual model of the prosthetic device placed in a proposed positionrelative to the portion of the dentition; calculating, with saidcomputer and models, the occlusal and interproximal relationship of thevirtual model of the prosthetic device relative to the virtual model ofthe portion of the dentition; wherein said step of calculating includes,for a plurality of points on a surface of a tooth, the step ofcalculating a sphere around each of said points, and enlarging the sizeof the sphere until the sphere intersects with a surface of said virtualmodel of the prosthetic device; adjusting the shape of the virtual modelof the prosthetic device so as to optimize the occlusal andinterproximal relationship of the virtual model of the prosthetic devicerelative to the virtual model of the portion of the dentition; andfabricating the prosthetic device.
 17. The method of claim 16, whereinthe prosthetic device comprises a crown.
 18. The method of claim 16,wherein the prosthetic device comprises an inlay.
 19. The method ofclaim 16, wherein the prosthetic device comprises a bridge.
 20. Themethod of claim 16, further comprising the step calculating, with saidcomputer and said models, distances between surfaces of said prostheticdevice and surfaces of an adjacent tooth in said virtual model of aportion of the dentition.
 21. The method of claim 20, further comprisingthe step of displaying on said user interface portions of said virtualmodel of said prosthetic device and portions of said adjacent toot inwhich said distances are less than a predetermined threshold.
 22. Themethod of claim 20, further comprising the step of displaying on saiduser interface portions of said virtual model of said prosthetic deviceand portions of said opposing tooth in which said distances are lessthan a predetermined threshold.
 23. The method of claim 16, furthercomprising the step calculating, with said computer and said models,distance between surfaces of said prosthetic device and surfaces of anopposing tooth in said virtual model of a portion of the dentition. 24.A method of designing and fabricating a set of dentures for a patientand improving interproximal and occlusal contact of the teeth of saiddentures, comprising the steps of: storing a three-dimensional virtualmodel of teeth of upper and lower arches of the patient in a computer,wherein said teeth comprise template teeth stored in said computer;moving the teeth of the upper and lower arches to form a proposedarrangement for said set of dentures; calculating distances betweensurfaces of adjacent teeth and between surfaces of opposing teeth withthe upper and lower arches in a closed condition to assess theinterproximal relationship and occlusal contacts of said teeth; whereinsaid step of calculating includes, for a plurality of points on asurface of a tooth, the step of calculating a sphere around each of saidpoints, and enlarging the size of the sphere until the sphere intersectswith a surface of another adjacent or opposing tooth; displayinginformation associated with said calculations on a user interface;adjusting the position of one or more teeth to more optimally positionof said teeth relative to each other as a result of said display; andfabricating the dentures.
 25. The method of claim 24, wherein the stepof displaying information comprises the step of displaying portions ofadjacent or opposing teeth in a contrasting color or shading for whichthe distance between said portions is less than a predeterminedthreshold.